MB3 Multiple Phase Mass Balances

Mass Balance: Multi-Phase
MB3
Chemical Engineering
www. Chemical Engineering Guy .com

Content
• Section 1
– Single Phase Theory (Phase-Diagrams)
– Vapor Pressure (Antoine and Clapyeron Eqn)
– Gibbs Phase Rule
• Section 2
– Gas-Liquid Systems (1 condensable)
• Evaporation, Drying, Humidity
– Gas-Liquid Systems (multi-condensable)
• Raoult Law, Henry Law
• Dew/Bubble points
• Txy & Pxy Diagrams
• Section 3
– Solid-Liquid Systems
• Crystallization
– Solubility and Saturation
– Hydrated Salts
– Liquid-Liquid Systems
• Miscibility and Extraction

Application in MB
• Many processes include multiple-phase
equilibriums
– Humidity in air
– Absorption
– Distillation

Application in MB

Section 1
• Single Phase Theory (Phase-Diagrams)
– Phase Diagram
– Phase Change
– Boiling point (T,P); Sublimation point (T,P); Freezing point (T,P)
– L-S, L-G, G-S Equilibrium lines
• Vapor Pressure (Antoine and Clapyeron Eqn)
– Vapor pressure definition
– Volatility
– Latent heat of vaporization
– Vapor Pressure estimation/calculation
• Gibbs Phase Rule
– DOF for systems (intensive properties)

Phase Diagrams
• Diagram of a pure substance
– It’s a Plot containing one system variable
(P,T,V,etc.) vs. other one.
– It shows conditions at which the substance exists
in different phases (sol., liq., gas typically)

Phase Diagrams
• P-T Diagram shows the next information:
– Pressure of substance (y-axis)
– Temperature of substance (x-axis)
– Phase Equilibrium Lines
– Critical Point
– Triple Point
– Phases

Phase Diagrams

Special Data
• Phase Equilibrium Lines
– Phase equilibrium @ P,T
• Critical Point
– Point where no phase boundaries exist
• Triple Point:
– Point which the three equilibrium
lines meet
– Solid-Liquid-Gas coexist
• Boiling point
– Normal BP (P=1atm)
• Freezing point
– Normal FP (P=1atm)
• Sublimation point
– Normal SP (P=1atm)

Phase Diagrams
A phase diagram for a binary
system displaying a eutectic point.
The iron–iron carbide (Fe–Fe3C) phase diagram

Volatility and Vapor Pressure
• Volatility
– degree to which the species trends to transfer
from the liquid (or even solid) state to the vapor
state
• Vapor pressure Pº
– Measure of volatility
– Function of Temperature

Vapor Pressure
• Pressure exerted by a vapor in
thermodynamic equilibrium with its
condensed phases (solid or liquid) at a given
temperature in a closed system P
v
a
p
o
r
P
c
o
n
d

Vapor Pressure
• Given (T boiling)
• The Vapor Pressure “line” is shown in the
Graphic
• For any Tb, there is a Vapor Pressure

Estimation of Vapor Pressures
• Three types of estimation
– Clasius-Clapeyron Equation
– Antoine Equation
– Cox Diagrams

Clasius-Clapeyron Equation
• This approach supposes “straight” equilibrium
lines
Review Equilibrium Thermodynamics Course for Extra information in this topic

lines
“Straight line in intervals”

lines
• dp/dT = slope of line

• Vg-Vl = V^
• Substituting Ideal Gas
Law
• Inverting Temperature
axis (T  1/T)
• Logarithm of P-axis
• Suppose ΔH^v = cte.

• Ln P* vs. 1/T graphs
• Straight line
• Slope = ΔH^v/R
• Y-Intersect = B

• P* = Vapor Pressure [mm Hg]
• ΔH^v = Heat of Vaporization [J/gmol]
• R = Ideal gas constant
• T = (K)
• B= Intersection of Y-Axis constant
• You now just need 2 points to get parameters: B, ΔHv
• 2 vapor pressure points (Pº, T)

• What is latent heat of vaporization?
– Required energy to transform a mol of “liquid” to
a mol of “Vapor”
• ΔH^v = Heat of Vaporization [J/gmol]

Exercise 1
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Antoine Equation
• Empirical equation
• Similar to Clasius-Clapeyron Eqn.
• A,B,C values can be found in tables!
• p* must be expressed in mm Hg
• T must be expressed in ºC NOT K!

Antoine Equation
Exercise
• Calculate Pº of Acetone
– @ T = 20 ºC
– @ T = 240 ºC
Low Temp
High Temp
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Cox Diagrams
• Set of lines ending in Critical Points
• Y-axis typically Vapor pressure
• X-Axis typically Temperature of gas
• Recommended if using those set of
substances

Cox Diagrams
• Set of lines ending in Critical Points
• Y-axis typically Vapor pressure
• X-Axis typically Temperature of gas
• Recommended if using those set of substances
• Procedure:
– Choose a Substance
– Specify either P or T… Cross a horizontal line if P, vertical if T.
– Cross it with the line of the substance
– Make a Vertical line (if you started with P) or a horizontal line (if
you started with T).

Cox Diagrams
Pº for Ethylene at -50ºC

Cox Diagrams
Pº = 200 psi
Pº for Ethylene at -50ºC

Cox Diagrams
This line marks the 14.7 psi (atmospheric) “Normal” Boiling Point of Substances

Cox Diagrams
• Chinese Database

Need more Exercises & Problems?
• Go to www.ChemicalEngineeringGuy.com
• Section: Courses
– Mass Balance Course
• Problems Section
• You will find a problem index there…

Gibbs Phase Rule
• The number of intensive variables that can be
specified independently for a system at equilibrium:
• Π = Number of phases in the system
• c = Number of chemical Species
• DOF= Degrees of Freedom
• A system is completely stated if there are 0 DOF

Gibbs Phase Rule
Exercise
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Gibbs Phase Rule Conclusion
• Gibss Phase Rules is helpful to determine the variables in a
system
• In mixture systems, sometimes you need to “set” some
variables
We “fixed” P = 1 atm We “fixed” C = 1 substance

Gibbs Phase Rule Conclusion
• “Fixing” a property… P,V or T will
reduce the 3-D chart to a 2-D chart
(easier to read)
• Limitation  only that Value of
fixed variable (E.g. P= 1 atm, 1 m3)

End of Section 1
• We´ve seen
– Single Phase Theory (Phase-Diagrams)
• Pressure of substance (y-axis)
• Temperature of substance (x-axis)
• Phase Equilibrium Lines
• Critical Point
• Triple Point
• Phases
– Vapor Pressure
• Cox Diagrams
• Antoine Empirical Equation
• Clapyeron Theoretical Equation
– Gibbs Phase Rule
• Intensive Variables in a system

Section 2
• Gas-Liquid Systems (1 condensable)
– Only one substance condenses
– Evaporation, Drying, Humidity
– Examples: Air-Humidity
• Gas-Liquid Systems (multi-condensable)
– Raoult Law
– Henry Law
– Dew/Bubble points
– Txy & Pxy Diagrams
– Examples: Ethanol-Water

Gas-Liquid Systems: One Condensable
• Typical Example: Air+Humidity
• Air is non-condensable gas
• Humidity is a condensable vapor
• Typical operations:
– Evaporation
– Drying
– Humidification/dehumidification

• Liquid Water + Dry Air @ 75ºC and 1 atm
– Initially Dry Air has no water (yw = 0)
– Then, water evaporates to Dry Air (yw =/ 0)
– There is a partial pressure of water in the system
• Pw = yw·P
– At one point, water stops to evaporate
– At this point, the Air-Water mixture is “Saturated”

• Saturated system (DA+W):
– It contains all the water that system can hold at
that temperature and pressure
• Saturated vapor (W):
– Water evaporated contained in this type of system

• Apply Gibbs Phase Rule:
– DOF= 2 + c - π = 2+2-2 = 2
– We need to set 2 variables!
• T, P and yw  3 variables
• If we set P (1 atm) and T (temperture) you will
always be able to calculate yw
• If we set P (1 atm) and (yw) you will always
have the same temperature for the desired
system

Raoult Law (Single Component)
• If only one component will condense with
Temperature decrease…
• We may apply Raoult Law (for single
component!)

Raoult Law (Single Component
Exercise 1
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From Raoult’s law:
yw·P = P*
yw = P* / P
From tables/data bases
yw = 289 mm Hg / 760 mm Hg = 0.38 gmol W / gmol mix
yw = 0.38 gmol W / gmol mix
1 = yw + yda  yda = 1- yw = 1- 0.38 = 0.62 gmol DA /
gmol mix

Dew/Bubble Point
• Dew Temperature: temperature at which a
vapor becomes saturated (@ P = cte)
– The point at which the mix will start condensing
• Bubble Temperature: temperature at which a
liquid becomes saturated (@ P = cte)
– The point at which the mix will start evaporating
• NOTE  Dew Temp. = Bubble Temp. (#)

Dew/Bubble Point
• Bubble  you reach from liquid to vapor (blue)
• Dew  you go from vapor to liquid (red)
@ P =cte = 1 atm

Raoult Law (Single Component) MB
Exercise
1) DP = 90ºC … 100-90 = 10ºC

Raoult Law (Single Component) MB
Exercise
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Humidity Theory
• Types of Humidity/Saturation
– Relative
– Molal
– Absolute
• Psychometric Charts!
– Air and Humidity charts @ 1 atm

Relative Saturation
• Compares Partial Pressure of Water vs. Vapor
pressure of Water at that Temperature
• Typical for weather reports
• 40 % humidity; 80% humidity

Molal Saturation (Humidity)
• Moles of Vapor per Moles of Dry-Air
• Example:
– Moles of W = 2 gmol of Water
– Moles of Air = 180 gmol of Dry Air
– 2/180 = 0.01 gmol of W / gmol of DA
• This is NOT mole Fraction

Absolute Saturation (Humidity)
• Similar to Molal Saturation, compares mass of vapor
to mass of Dry gas
• Example:
– 0.05 kg of vapor
– 2 kg of dry air
– 0.05/2 = 0.025 kg of W / kg of DA
• This is NOT mass fraction of vapor in mixture!

Humidity Theory
• Eventually, you should find either:
– Partial Pressure of Vapor
– Mole fraction of Vapor in mixture
• With these data you could start MB

Saturation/Humidity
Exercise
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Psychometric Chart
• As seen before, the system of Dry Air and
Humidity have 2 DOF
• T,P, yw  Variables
• If we set P = 1 atm we would only need to
define either T or yw
• A graph already exists! Its called Psychometric
Chart and relates humidity and temperature
of air

Psychometric Chart
• We found the next variables
– Specific volume of dry air [m3/kg DA]
– Dry bulb temperature [ºC]
– Wet bulb temperature [ºC]
– Relative humidity [%]
– Absolute humidity [kg w / kg DA]

Psychometric Chart
High
Temperatures

Psychometric Chart
Low
Temperatures

How to read a Psychometric Chart
Absolute
Humidity

Relative
Humidity

Dry Bulb
Temperature

Wet Bulb
Temperature

Specific
Volume of DA

We need at least two:
- 1 temp + 1 humid
- 2 temp
- 2 humid
• We need:
– Set a Temperature (any)
• Dry
• Wet
– Set a Humidity (any)
• Relative
• Absolute
NOTE: Setting Specific Volume of DA indirectly sets a Temperature… WHY?

Exercise
• What is the Relative humidity of a stream of air @
30ºC and 0.007 kg of moisture per kg of DA
• Locate Temperature (x axis)
• Locate Absolute Humidity (y axis)
• Locate Relative Humidity (probably between two lines)

Exercise

Exercise
• Between 20% and
30%
• Relative Humidity is
Approx. 28%

Dry Bulb Temperature
• Temperature of air measured by a
thermometer freely exposed to the air but
shielded from radiation and moisture
• Generally known as “THE” temperature of air.
• It is the true thermodynamic temperature
• Does not indicate the amount of moisture in
the air

Wet Bulb Temperature
• Temperature that air would have if it were cooled
to saturation (100% relative humidity)
– By evaporation of water
– Latent heat being supplied by air
• The lowest temperature that can be reached
under current ambient conditions by the
evaporation of water only
• Its determined by
– Actual air temperature (dry-bulb temperature)
– Amount of moisture in the air (humidity).

Dry/Wet Bulb Temperature
• Dry Bulb Thermometer has no add-ons
• Wet Bulb Thermometer has a “wet” coat so water may
vaporize

Break
 We’ve Seen
We’ve Seen 
What's Left 
 What's Left

Gas-Liquid: Multicomponent
• Processes which involve 2+ components in at
least 2+ phases
• Typical processes
– Vapor-Liquid  Distillation & Absorption
– Solid-Liquid  Solutions (Crystallization)
– Liquid-Liquid  Immiscible liquids (Extraction)

Vapor-Liquid Equilibrium
• Best way to evaluate equilibriums  Data
• If we got no data  estimate

Exercise 1

Exercise 1
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• What if we got NO data?
• We need to apply some Laws
– Raoult Law
– Henry Law
• These law help relate vapor pressures with
concentrations (mole fractions) and constants
• Using Gibbs Rule
– DF = 2 – c – π = 2 – 2 -2 = 2
– We need two variables!
2 phases
2 substances

Raoult Law
• If ideal solution (one that follows Roult Law)
– Xa  1 (A is almost pure)
• Then we can relate liquid phase with vapor
phase:
ya = mole fraction of A in vapor
P = Total pressure of system
xa = mole fraction of A in liquid
Paº(T) = Vapor Pressure of A
• Note, if we set A, then B is fixed too WHY?

Raoult Law
• Remember Raoult law for 1 condensable?
• This equation 
• Reduces to 
Xa = 1
Ya = 1

Henry Law
• Ha(T): Henry Constant
• Valid when Xa  0 (when it is dilute)
– Suppose no dissociation, ionization, reaction

Raoult and Henry Law
Exercise
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Exercise
Xb = Xt
(equimolar)
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Exercise
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• Continue to solve for yb and P

Exercise
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• Substitute yb in P equation… you get P

Dew/Bubble Point
• We’ve seen Dew and Bubble Temperatures
– Typical for Equilibrium Thermodynamics
– Calculating Temperature of the Dew Point
– Calculating Temperature of the Bubble Point
• Visit  www.ChemicalEngineeringGuy.com/Courses
– Click on Courses  Equilibrium Thermodynamics

Graphical Representation:
• We use diagrams to condense data:
– T x-y Diagrams: Temperature vs. compositions
– P x-y Diagrams: Pressure vs. compositions
• We use this on Binary Systems (A+B)
• If Txy  fix P (generally 1 atm)
• If Pxy  fix T (Temperature may vary)

T x-y Diagrams
• Simplest form of
T x-y Diagrams
• Y-axis: Temperature
• X-Axis: Mole
Composition of A
• Vapor Region
• Liquid Region

T x-y Diagrams

P x-y Diagrams
• Simplest form
of P x-y
Diagrams
• Y-axis: Pressure
• X-Axis: Mole
Composition of
A
• Vapor Region
• Liquid Region

P x-y Diagrams

P x-y Diagrams
More Information of P xy and T xy Diagrams in Equilibrium Thermodynamics Course

T x-y and P x-y Diagrams
Exercise 1
We don’t need P xy (WHY?)
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Exercise 1
a) Temperature
when boiling…
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Exercise 1
a) Temperature
when boiling…
T boiling approx= 86ºC
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Exercise 1
b) Final
Composition?
Boiling @ T
constant (WHY)
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Exercise 1
Boiling @ T
constant (WHY)
YB = 0.87
b) Final
Composition?
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End of Section 2
• Section 2
– Gas-Liquid Systems (1 condensable)
• Evaporation, Drying, Humidity
• Theory of Humidity (absolute, molal, relative)
• Raoult Law for 1 condensable specie
• Psychometric Charts
• MB with G-L (1) data
– Gas-Liquid Systems (multi-condensable)
• Vapor-Liquid Equilibrium
• Raoult Law
• Henry Law
• Txy & Pxy Diagrams
• MB with G-L (2+) data

Section 3
• Section 3
• Crystallization
– Hydrated Salts

Solid-Liquid Systems
• MB processes  Crystallization
– Solution, Solvent, Solute
– Saturated and Supersaturated concepts
– Hydrated Salts

Solubility
• Solubility of a solid in a liquid is the maximum
amount of that substance that can be solved
in a specific amount of liquid (in equilibrium)
• Varies for each type of substance
• Is Temperature Dependent

Solubility of Some Substances
Solubility of some common salts

Unsaturated Solution
• Unsaturated solution:
– is a chemical solution in which the solute
concentration is lower than its equilibrium
solubility.

Saturated Solution
• Saturated solution:
– is the point at which a solution of a substance can
dissolve no more of that substance and additional
amounts of it will appear as a separate phase
Any more solute will stay as a solid

Supersaturated Solution
• Supersaturated solution
– is a state of a solution that contains more of the
dissolved material than could be dissolved by the
solvent under normal circumstances.
Crystals form in a supersaturated solution

Crystallization MB
exercise 1
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Hydrated Salts
• Anhydrous salts: Water free salts
• Hydrated Salts: Salts + Hydrate
– Water molecules bon to the salt

Hydrated Salts
Exercise
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Hydrated Salts
Exercise
60 kg K per 100 kg W
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Hydrated Salts
Exercise
• See next diagram for solution
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Hydrated Salts
Exercise
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About 75ºC (Saturation Temp.)

Colligative Properties
• This topic is covered in
– Basic Chemistry Course
– Equilibrium Thermodynamics
• The scope of our course does not includes
such material

Liquid-Liquid Systems
• Miscibility and Immiscibility
• Partially miscible
• Liquid Extraction
• Distribution Coefficient

Extraction
• Miscibility
– property of substances to mix in all proportions,
forming a homogeneous solution
– Miscible
– Partially Miscible
– Not Miscible

Extraction
• LLE consists in transferring one (or more)
solute(s) contained in a feed solution to
another immiscible liquid (solvent).
• The solvent that is enriched in solute(s) is
called extract.
• The feed solution that is depleted in solute(s)
is called raffinate.

Extraction
• Extraction
• Distribution
Coefficient/Partition ratio
– Ralates transfer

Extraction
• In practice, extraction is often carried out in
several consecutive stages.
• The solution leaves each stage and then goes
to another additional solvent in the next stage
• Enough stages should be used to achieve
almost a complete transfer of solute

Exercise 1
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End of Section 3
• Section 3
• Crystallization
– Hydrated Salts

Problems & Exercises
• All pair problems of Elementary Principles in Chemical
Processes. Felder, R; Rousseau, R. 3rd edition are solved in the
next videos. (Chapter 6)
• Remember: practice makes the master

Elementary Principles in Chemical
Processes
What topics did we covered from the book?

End of MB3: Multiple-Phase MB
• You should be now able to perform MB with multiple phases
• Hopefully you are now able to:
– Understand phases
– Calculate Vapor pressure and apply them in MB
• Clasisus Clapeyron
• Antoine Equation
– Get to know the Vapor-Liquid equilibrium systems
– Use Raoult Law and Henry Law
– Understand the Solid-Liquid system
– Solve Liquid Liquid systems

MORE INFORMATION
• Get extra information here!
• FB page:
– www.facebook.com/Chemical.Engineering.Guy
• Contact me by e-mail:
– Chemical.Engineering.Guy@gmail.com
• Directly on the WebPage:
– www.ChemicalEngineeringGuy.com/courses

Bibliography
• Elementary Principles in Chemical Processes. Felder, R;
Rousseau, R. 3rd edition.
• Basic Principles and Calculation in Chemical Engineering.
Himmelblau, D. 7th edition.

MB3 Multiple Phase Mass Balances

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MB3 Multiple Phase Mass Balances